Author: Shane TurnbullPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Competition Within Random Growth Models
Author: Shane TurnbullRandom Growth Models
Author: Michael DamronPublisher: American Mathematical Soc.
ISBN: 1470435535
Category : Mathematics
Languages : en
Pages : 274
Book Description
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Stochastic Models of Growth and Competition
Author: Richard DurrettRandom Fluctuations and Pattern Growth: Experiments and Models
Author: Harry Eugene StanleyPublisher: Springer Science & Business Media
ISBN: 9400926537
Category : Science
Languages : en
Pages : 366
Book Description
Proceedings of the NATO Advanced Study Institute, Cargèse, Corsica, France, 18-31 July, 1988
Competition and Growth
Author: Philippe AghionPublisher: MIT Press
ISBN: 0262512025
Category : Business & Economics
Languages : en
Pages : 115
Book Description
Though competition occupies a prominent place in the history of economic thought, among economists today there is still a limited, and sometimes contradictory, understanding of its impact. In Competition and Growth, Philippe Aghion and Rachel Griffith offer the first serious attempt to provide a unified and coherent account of the effect competition policy and deregulated entry has on economic growth. The book takes the form of a dialogue between an applied theorist calling on "Schumpeterian growth" models and a microeconometrician employing new techniques to gauge competition and entry. In each chapter, theoretical models are systematically confronted with empirical data, which either invalidates the models or suggests changes in the modeling strategy. Aghion and Griffith note a fundamental divorce between theorists and empiricists who previously worked on these questions. On one hand, existing models in industrial organization or new growth economics all predict a negative effect of competition on innovation and growth: namely, that competition is bad for growth because it reduces the monopoly rents that reward successful innovators. On the other hand, common wisdom and recent empirical studies point to a positive effect of competition on productivity growth. To reconcile theory and evidence, the authors distinguish between pre- and post-innovation rents, and propose that innovation may be a way to escape competition, an idea that they confront with microeconomic data. The book's detailed analysis should aid scholars and policy makers in understanding how the benefits of tougher competition can be achieved while at the same time mitigating the negative effects competition and imitation may have on some sectors or industries.
Non-equilibrium Surface Growth for Competitive Growth Models and Applications to Conservative Parallel Discrete Event Simulations
Author: Poonam Santosh VermaPublisher:
ISBN:
Category : Computer algorithms
Languages : en
Pages :
Book Description
Non-equilibrium surface growth for competitive growth models in (1+1) dimensions, particularly mixing random deposition (RD) with correlated growth process which occur with probability p are studied. The composite mixtures are found to be in the universality class of the correlated growth process, and a nonuniversal exponent _ is identified in the scaling in p. The only effects of the RD admixture are dilations of the time and height scales which result in a slowdown of the dynamics of building up the correlations. The bulk morphology is taken into account and is reflected in the surface roughening, as well as the scaling behavior. It is found that the continuum equations and scaling laws for RD added, in particular, to Kardar-Parisi-Zhang (KPZ) processes are partly determined from the underlying bulk structures. Nonequilibrium surface growth analysis are also applied to a study of the static and dynamic load balancing for a conservative update algorithm for Parallel Discrete Event Simulations (PDES). This load balancing is governed by the KPZ equation. For uneven load distributions in conservative PDES simulations, the simulated (virtual) time horizon (VTH) per Processing Element (PE) and the simulated time horizon per volume element Nv are used to study the PEs progress in terms of utilization. The width of these time horizons relates to the desynchronization of the system of processors, and is related to the memory requirements of the PEs. The utilization increases when dynamic, rather than static, load balancing is performed.
Competition Theory in Ecology
Author: Peter A. AbramsPublisher: Oxford University Press
ISBN: 0192648098
Category : Science
Languages : en
Pages : 336
Book Description
Competition between species arises when two or more species share at least some of the same limited resources. It is likely to affect all species, as well as many higher-level aspects of community and ecosystem dynamics. Interspecific competition shares many of the same features as density dependence (intraspecific competition) and evolution (competition between genotypes). In spite of this, a robust theoretical framework is not yet in place to develop a more coherent understanding of this important interaction. Despite its prominence in the ecological literature, the theory seems to have lost direction in recent decades, with many synthetic papers promoting outdated ideas, failing to use resource-based models, and having little utility in applied fields such as conservation and environmental management. Competition theory has done little to incorporate new findings regarding consumer-resource interactions in the context of larger food webs containing behaviourally or evolutionarily adapting components. Overly simple models and methods of analysis continue to be influential. Competition Theory in Ecology represents a timely opportunity to address these shortcomings and suggests a more useful approach to modelling that can provide a basis for future models that have greater predictive ability in both ecology and evolution. The book concludes with some broader observations on the lack of agreement on general principles to use in constructing mathematical models to help understand ecological systems. It argues that a more open discussion and debate of the underlying structure of ecological theory is now urgently required to move the field forward.
Competition and Growth
Author: J. K. SenguptaPublisher: Springer
ISBN: 0230505317
Category : Business & Economics
Languages : en
Pages : 185
Book Description
Jati K. Sengupta examines the market dynamics of the evolution of industry and the impact of new technology with R&D and knowledge capital. The book builds the theory of innovations in the contexts of the high-tech industries of today such as computing and telecommunications.
A Biologist's Guide to Mathematical Modeling in Ecology and Evolution
Author: Sarah P. OttoPublisher: Princeton University Press
ISBN: 1400840910
Category : Science
Languages : en
Pages : 745
Book Description
Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
Mathematical Ecology
Author: Thomas G. HallamPublisher: Springer Science & Business Media
ISBN: 3642698883
Category : Mathematics
Languages : en
Pages : 455
Book Description
There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.